- #1

Phoeniyx

- 16

- 1

Hey guys. This question is really bugging me. (Please see question #63 here: http://www.ets.org/s/gre/pdf/practice_book_math.pdf) - written below for your convenience.

[itex]f(x) = xe^{-x^{2}-x^{-2}}, x \neq 0[/itex]

[itex]f(x) = 0, x = 0 [/itex]

(apologies for not knowing the itex command do write this as a single f(x))

The question is, at how many values of [itex]x[/itex] does the graph of f(x) have a horizontal tangent line?

My answer was "two" and the correct answer is "three".

For those of you that like a challenge, only 14% of the testers answered this correctly and is the least correctly answered question of the whole test.

Differentiating f(x) at all x != 0 would yield two real results (and two imaginary results - which is ignored). The real question IMO is what happens at x == 0.

As [itex]x[/itex] approaches 0+, f(x) tends to 0+ and as [itex]x[/itex] approaches 0-, f(x) tends to 0-(since the exponential tends to 0 either way).

So, how can there be a horizontal tangent line at 0? Thanks!

[itex]f(x) = xe^{-x^{2}-x^{-2}}, x \neq 0[/itex]

[itex]f(x) = 0, x = 0 [/itex]

(apologies for not knowing the itex command do write this as a single f(x))

The question is, at how many values of [itex]x[/itex] does the graph of f(x) have a horizontal tangent line?

My answer was "two" and the correct answer is "three".

For those of you that like a challenge, only 14% of the testers answered this correctly and is the least correctly answered question of the whole test.

Differentiating f(x) at all x != 0 would yield two real results (and two imaginary results - which is ignored). The real question IMO is what happens at x == 0.

As [itex]x[/itex] approaches 0+, f(x) tends to 0+ and as [itex]x[/itex] approaches 0-, f(x) tends to 0-(since the exponential tends to 0 either way).

So, how can there be a horizontal tangent line at 0? Thanks!

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